Remark 4 Ref. [1]} proposes an exactly convergent algorithm for a uniform quantizer without convergence rate analysis by directly combining algcon2 with a gradient step in the update of \(X^{k+1}\) , which is improved in [2]} with an explicit sublinear convergence rate. Then, linear convergence is achieved in [3]}, [4]}, [5]} by designing specified time-varying uniform compressors. In contrast, Dyna-COLD converges linearly for a class of compressors.

